Non-destructive techniques are used widely in the metal industry in order to control the quality of materials. Eddy current testing is one of the most extensively used non-destructive techniques for inspecting electrically conductive materials at very high speeds that does not require any contact between the test piece and the sensor. This paper includes an overview of the fundamentals and main variables of eddy current testing. It also describes the state-of-the-art sensors and modern techniques such as multi-frequency and pulsed systems. Recent advances in complex models towards solving crack-sensor interaction, developments in instrumentation due to advances in electronic devices, and the evolution of data processing suggest that eddy current testing systems will be increasingly used in the future.

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Non-Destructive Techniques Based on Eddy Current Testing

Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid

On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation

In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley–Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

Solution of fractional differential equations by using differential transform method

Review of utilization of genetic algorithms in heat transfer problems

Solution of boundary value problems for integro-differential equations by using differential transform method

In this study, fractional differential transform method (FDTM), which is a semi analytical numerical technique, is extended to solve fractional integro-differential equations of Volterra type. New theorems for the transformation of integral terms having degenerate kernels that never existed before are introduced with their proofs. This implemented new technique is validated by solving and comparing four different examples that exist in the literature. It is observed that, FDTM can be utilized as a powerful and reliable tool for the solution of fractional integro-differential equations.

Solution of fractional integro-differential equations by using fractional differential transform method

In this study, differential transform method (DTM) is applied to both integro-differential and integral equation systems. The method is further expanded with a formulation to treat Fredholm integrals. If the system considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. So as to show this capability and robustness, some systems of integral and integro-differential equations are solved as numerical examples.

Ibrahim Ozkol

Papers

Solution of fractional differential equations by using differential transform method

Solution of boundary value problems for integro-differential equations by using differential transform method

Solution of fractional integro-differential equations by using fractional differential transform method

Solutions of integral and integro-differential equation systems by using differential transform method

Solution of difference equations by using differential transform method